5.4 TI Precision Labs - Op Amps: Bandwidth - AOL gain slew rate

Hello and welcome to the TI Precision Lab discussing Op Amp Bandwidth, Part 4. In this video we'll cover five bandwidth related topics. First, a deeper look at how the slope of the AOL curve affects gain bandwidth. Second, how an op amps input capacitance can limit the bandwidth. Third, how to calculate the practical gain versus frequency for amplifier circuits. Fourth, how to limit the bandwidth of a circuit using a feedback capacitor. And finally, how slew rate can affect the circuit's response over frequency.
At this point, we have discussed the gain bandwidth product in great detail. We know that it is only valid where the slope of the AOL curve is minus 20 dB per decade. Unfortunately, sometimes it is not obvious whether the gain bandwidth product is valid or not.
Here we have the gain bandwidth product specification from the OPA 209 data sheet. The typical gain bandwidth product is listed as 18 megahertz, given that the gain is 1 volt per volt. But what about for other closed loop gains?
Here we have the open loop gain and phase curve versus frequency from the data sheet. The open loop gain curve appears to be linear, and decreasing at a constant rate of minus 20 dB per decade. Thus, one might assume that the gain bandwidth product is valid for all closed loop gains.
However, simulation and real world measurements will show that such an assumption is incorrect. Why? Previously, we assumed that the open loop gain curve had a constant slope of minus 20 dB per decade. However, we find that there's a small bend in the AOL curve between 1 megahertz and 10 megahertz due to a pole zero pair.
A pole near 1 megahertz causes the open loop gain to decrease faster than minus 20 dB per decade over a small range of frequency. But the pole is then quickly canceled by a 0. Due to the logarithmic scale, it is not possible to see this small bend in the AOL curve. As a matter of fact, the bend is probably smaller than the thickness of the line in the curve.
Zooming in on the bend in the curve, you will notice that the gain bandwidth is 18 megahertz at the specified gain of 1 volt per volt, but increases to 23.7 megahertz for closed loop gains greater than 20 dB. While the bend in the AOL curve is difficult, if not impossible, to see, the pole 0 pair is more apparent in the phase curve. Notice the dip in the phase curve near 1 megahertz. This is due to the pole zero pair. Therefore, it is recommended that one always inspect the phase curve in addition to the gain curve in an op amp data sheet.
These two curves depict how the gain bandwidth product changes with frequency and closed loop gain. Notice that at a closed loop gain of 0 dB, or 1 volt per volt, the gain bandwidth product is 18 megahertz, as stated in the data sheet. As the closed loop gain increases, the bandwidth increases to 23.7 megahertz.
Ultimately there are three lessons to learn from this discussion. First, it is not unusual to see some deviation in gain bandwidth for different closed loop gains, and that the amount of deviation will vary depending on the amplifier.
Second, the phase curve is key to locating the existence of a pole 0 pair. So always be sure to inspect the phase curve in addition to the open loop gain curve.
Finally, don't expect the exact bandwidth performance listed in the data sheet. Typical bandwidth specifications can vary by approximately plus or minus 30% over process, and an additional plus or minus 30% over temperature. Therefore, it is highly recommended to include significant margin for bandwidth in your design.
Up to this point we have seen how the op amps gain bandwidth limitation sets the bandwidth. However, in some cases, other factors can affect bandwidth. This slide focuses on the effect of input capacitance on bandwidth.
All op amps will have a differential and common mode input capacitance and impedance. This parasitic capacitance is from the semiconductor junctions on the input stage transistors. The differential capacitances connected between the two inputs and the common mode capacitance is connected on each input with respect to AC ground.
The table at the top of the slide shows how input capacitance is typically specified. In this example, the differential capacitance is 1.6 picofarads. And the common mode capacitance is 6.4 picofarads. These input capacitances are relatively small. So it is unlikely that you will see bandwidth limitations, unless the input signal source has a large series resistance.
In this example, the source resistance is 1 megaohm, which is relatively large. The source resistance and common mode input capacitance form a low pass filter. The corresponding cutoff frequency is calculated to be 24.87 kilohertz.
Notice that the differential capacitance and the common mode capacitance on the inverting input are not included in the bandwidth calculation. This is because the op amp feedback eliminates the effect of these capacitances. The input capacitance is part of TI's op amp macro models. So let's take a look at some simulation results.
This slide shows an AC transfer characteristic sweep for the OPA 192. Based on the gain bandwidth of the device and the circuit's closed loop gain of 100 volts per volt, or 40 dB, we expect 100 kilohertz of bandwidth. Our simulation, however, yields a bandwidth of 24.46 kilohertz. This discrepancy is due to the low pass filter formed by the one megaohm source resistance, and the 6.4 picofarad common mode input capacitance.
In this example, the hand-calculated bandwidth of 24.87 kilohertz correlates with the simulated bandwidth of 24.6 kilohertz. Now let's discuss how to calculate the practical gain of an op amp circuit. It is often assumed that the closed loop gain of an amplifier circuit is constant until it starts to roll off at the cutoff frequency.
In reality, the closed loop gain begins to decrease long before the cutoff frequency. The error introduced by this attenuation is usually unexpected. The closed loop gain at any frequency can be calculated using this equation, where f is frequency, Gcl_dc is the DC closed loop gain, fdom is the dominant pole, beta is the feedback factor, and Aol_dc is the DC open loop gain.
Let's use this equation and apply it to the OPA 192 circuit. The closed loop DC gain is calculated using 126 db, which is the AOL specification from the OPA 192 data sheet, and the feedback factor, or beta, from the OPA 192 circuit. The dominant pole is calculated using this equation, which was given in a previous bandwidth video.
Now that we've calculated the closed loop DC gain and dominant pole frequency, we can use the given equation to calculate the closed loop gain at 10 kilohertz. Note that the bandwidth for the circuit is 100 kilohertz. So 10 kilohertz is well inside the bandwidth of the amplifier.
In this example, the hand-calculated closed loop gain is 99.5 volts per volt, which correlates well with the simulated closed loop gain of 99.56 volts per volt. Calculating the closed loop gain at DC yields 99.995 volts per volt, which is even closer to the theoretical value of 100 volts per volt.
Therefore, we can conclude that as frequency increases, the closed loop gain decreases as you approach the cutoff frequency. So if a design requires a precise gain at higher frequencies, the cutoff frequency should be increased accordingly.
So far we have considered internal op amp specifications such as gain bandwidth and input capacitance when determining a circuit's bandwidth. In some cases, it is desirable to use external components to limit bandwidth. One approach is to use active filters, which use complex RC combinations to create very effective filters. Active filters will be discussed in a separate series of videos.
A simpler method for limiting a circuit's bandwidth is by placing a capacitor in the feedback path. For this analysis, it is best to think of the capacitor as an open circuit for low frequencies, and a short circuit at high frequencies. At low frequencies, you can ignore the capacitor in the circuit. So the gain will be 100 volts per volt, or 40 dB.
At high frequencies, the capacitor will short the 99 kiloohm resistor. So the amplifier circuit will have a gain of one volt per volt, or 0 db. Between the low and high frequencies, the gain will roll off at a rate of minus 20 dB per decade. Note that at very high frequencies, the gain will roll off further because of the amplifier's bandwidth limitations.
Note that the cutoff frequency of the filter is set by the feedback capacitor and feedback resistor. The calculated value is 1.005 kilohertz, which correlates well with the simulated value of 989 hertz. It is important to note that the filter reduced the gain from 40 dB to 0 dB. The attenuation is dependent on the gain of the amplifier.
Let's take a closer look at this. This slide compares how the feedback capacitor filter works for amplifiers and high and low gain. In both cases, the cutoff frequency is set to the same value.
As mentioned before, at high frequency, the feedback capacitor filter effectively shorts the feedback resistor, which forces the gain to 1 volt per volt. So the feedback capacitor filter will always reduce the gain from the DC value to 1. Thus, the maximum attenuation of the filter equals the DC gain.
In the case of the high gain circuit, the gain is attenuated from 100 volts per volt to 1 volt, or 40 dB. The low gain circuit, however, only attenuates the gain by 6 dB. The point is that the feedback capacitor filter is most effective for higher gain circuits.
If you need an affective filter for low gain circuits, you should probably look into an active filter. In general, active filters are more effective than a feedback capacitor filter. But the feedback capacitor filters are popular because they are simple and inexpensive.
Finally, let's discuss slew rate and full power bandwidth. The slew rate of an op amp is the maximum rate of change of the output signal. If you're interested in learning about the details of slew rate, please view the slew rate video series.
The slew rate of a device can affect how an op amp behaves over frequency. And this effect can be misinterpreted as a bandwidth limitation. In fact, the maximum output voltage versus frequency depends on the slew rate, and is often called full power bandwidth.
Let's look at how the full power bandwidth affects two different signals applied to the OPA 192 unity gain follower. The graph of maximum output voltage versus frequency tells what maximum undistorted peak-to-peak output can be achieved at a given frequency.
For example, let's apply a 1-volt peak signal at a frequency of 1 megahertz. This signal is well below the maximum output limitation. So there should be no distortion. However, a 10-volt peak signal at a frequency of 1 megahertz is outside the full power bandwidth. So the signal will be distorted.
Now let's look at a time domain simulation to see how the output is affected in both cases. This slide shows the OPA 192 output with a 10-volt peak and 1-volt peak input at 1 megahertz. Notice that the output for a 1-volt peak input is 1 volt peak, as expected. Also, the 1-volt peak output does not appear distorted.
The output for the 10-volt peak input, however, is 5 volts peak, and appears very distorted. In fact, the output looks more like a triangle wave then a sinusoidal wave. This is often the case for amplifiers that are in slew rate limit. These results make sense based on the full power bandwidth graph from the previous slide.
One final thing to notice is that the input signal is well inside the bandwidth of the OPA 192 buffer. Sometimes, attenuation of the output signal caused by slew rate limitation is incorrectly interpreted as a bandwidth limitation. To avoid this problem, always make sure that your output signal amplitude does not violate the maximum output voltage versus frequency graph in the data sheet.
In summary, this video discussed how the slope of the AOL curve affects the gain bandwidth, op amp input capacitance, calculating the practical gain of the circuit, slew rate limitations, and some simple ways to implement an op amp filter. Thank you for your time. Please try the quiz to check your understanding of this video's content. 大家好，欢迎来到 TI 高精度实验室，本视频将介绍 运算放大器 带宽第 4 部分。 在本视频中，我们将讲述 五个与带宽相关的主题。 第一，深入了解 AOL 曲线的斜率 如何影响增益带宽。 第二，运算放大器 输入电容 如何能够限制带宽。 第三，如何计算 放大器电路的 实际增益和带宽。 第四，如何利用 反馈电容器 来限制电路的带宽。 第五，转换速率如何 能够影响电路的 频率响应。 现在，我们 已详尽讨论了 增益带宽积。 我们知道，它仅在 AOL 曲线的斜率 为 -20 dB/十倍频程 时才是有效的。 遗憾的是，有时候 增益带宽积 有效与否 并非很明显。 现在，我们有 OPA 209 数据表中给出的 增益带宽积规格。 当增益为 1 V/V 时， 典型的增益带宽积 被列为 18 MHz。 但其他闭环 增益是怎么样呢？ 现在我们有 数据表中给出的 开环增益和相位曲线 与频率的关系。 开环增益 曲线似乎是 线性的，以 -20 dB/十倍频程的 恒定速率下降。 因此，人们可能会假定 增益带宽积对于所有 闭环增益而言都是有效的。 然而，仿真和 实际测量 将会表明， 这一假定并不正确。 为什么？ 先前我们假定 开环增益曲线 有 -20 dB/十倍频程的 恒定斜率。 不过，我们发现 由于有一个零极点对， 因而 AOL 曲线在 1 MHz 与 10 MHz 之间有一个 小弯曲。 接近 1 MHz 的极点 在较小的频率范围内 造成开环增益 下降的速率大于 -20 dB/十倍频程。 但是，极点随后 很快被零抵消。 由于对数坐标， 不可能在 AOL 曲线上 看到这个小弯曲。 事实上， 此弯曲 可能比曲线中的 线条粗细还要小。 放大曲线的 弯曲处后， 您会发现， 在指定的 1 V/V 增益下， 增益带宽为 18 MHz， 但当闭环增益 大于 20 dB 时， 会增加至 23.7 MHz。 虽然 AOL 曲线中的 弯曲难以看到， 但相位曲线中的 零极点对 更为明显。 请注意接近 1 MHz 的 相位曲线倾斜。 这是由零极点对 导致的。 因此，建议大家除了 检查运算放大器 数据表中的 增益曲线之外， 也要检查 相位曲线。 这两条曲线 描述增益带宽积 是如何随着频率 和闭环增益变化的。 请注意，在 闭环增益为 0 dB 或 1 V/V 时， 数据表中所列的 增益带宽积 为 18 MHz。 当闭环增益 增加时， 带宽增加 至 23.7 MHz。 最后，从该 讨论中可以 了解到三点。 第一，看到增益 带宽在不同的 闭环增益中 有些偏差 并非个别情况， 而且偏差量 将因放大器而异。 第二，相位曲线 是定位零极点对 所在的关键。 所以，除了检查 开环增益曲线之外， 也一定要检查相位曲线。 第三，不要期望 数据表中会列出 确切的带宽性能。 典型带宽规格 在不同的制程中 会有约 ±30％ 的差异， 且在不同的 温度下另有 ±30% 的差异。 因此，强烈 建议设计时 对带宽要留有 显著的裕度。 至此，我们已经看到 运算放大器增益带宽 限制如何设定带宽。 然而，在某些情况下， 其他因素会影响带宽。 此幻灯片着重于 介绍输入电容 对带宽的影响。 所有的运算放大器 都有差模和共模 输入电容和阻抗。 这种寄生 电容是由 输入级晶体管的 半导体结造成的。 差模电容连接到 两个输入之间， 共模电容 相对于 交流接地 连接到各输入。 幻灯片顶部的 表格显示了 输入电容通常是 如何指定的。 在本示例中， 差模电容 是 1.6 pF， 且共模电容 是 6.4 pF。 这些输入电容 都比较小， 所以您不太可能 会看到带宽限制， 除非输入信号源 具有大串联电阻。 在本示例中， 源电阻 相对较大， 为 1 兆欧姆。 源电阻和 共模输入电容 构成低通滤波器， 计算出的 对应 截止频率 为 24.87 KHz。 请注意， 反相输入的 差模电容和 共模电容 未包括在 带宽计算中。 这是因为运算 放大器反馈消除了 这些电容的影响。 输入电容是 TI 的运算 放大器宏模型的一部分， 那么，让我们来看一下 一些仿真结果。 此幻灯片显示了 OPA 192 的 交流传输特性扫描。 根据器件的 增益带宽 和电路的 100 V/V 或 40 dB 闭环增益， 我们预估带宽 为 100 KHz。 但是，我们的仿真 只产生 24.46 KHz 的带宽。 这种差异是由 1 兆欧姆源电阻 和 6.4 pF 共模输入 电容构成的 低通滤波器导致的。 在本示例中， 24.87 KHz 的 手算带宽与仿真 得到的 24.6 KHz 的 带宽具有相关性。 现在，我们来探讨一下如何 计算运算放大器电路的 实际增益。 人们通常假设， 当放大器电路的 闭环增益开始 在截止频率处滚降之前， 该闭环增益 恒定不变。 实际上，环回增益 在截止频率之前 就开始降低。 由这种衰减引起的 误差通常是 意想不到的。 可使用此等式 计算在任何 频率下的闭环增益， 其中 f 表示频率， Gcl_dc 表示直流 闭环增益， fdom 表示主极点， β 表示反馈因子， 并且 Aol_dc 表示 直流开环增益。 让我们将此 等式应用于 OPA 192 电路。 闭环直流 增益使用 OPA 192 数据表中 给出的 AOL 规格 126 dB 和 OPA 192 电路中的反馈因子 或 β 计算。 主极点使用 此等式计算， 该等式在之前的 带宽视频中已给出。 既然我们已经 计算出闭环直流增益 和主极点频率， 我们便可以 使用给定等式 来计算 10 KHz 的 闭环增益。 注意，该电路的 带宽为 100 KHz， 因此 10 KHz 稳妥地 落在放大器带宽内。 在本示例中， 手算的闭环 增益是 99.5 V/V， 与仿真得出的 99.56 V/V 闭环 增益具有相关性。 计算直流 闭环增益 得出 99.995 V/V， 更接近 100 V/V 的 理论值。 因此，我们可以得出结论， 即随着频率的增加， 当接近截止 频率时，闭环 增益减小。 所以，如果设计 需要在更高 频率下的 精确增益， 则应相应地增大截止频率。 到目前为止，在确定 电路的带宽时， 我们已考虑内部 运算放大器规格， 如增益带宽 和输入电容。 在某些情况下， 使用外部组件来 限制带宽较为理想。 一种方法是使用 有源滤波器， 该滤波器使用复杂的 RC 组合 来打造非常有效的滤波器。 我们将在另外一个视频 系列中讨论有源滤波器。 限制电路带宽的 一个更简单的方法 是在反馈路径中 放置一个电容器。 对于这种分析， 最好把电容器看作 低频下的 开路 和高频下的 短路。 在低频时， 您可以 忽略电路中的电容器。 因此，增益将为 100 V/V 或 40 dB。 在高频时，电容器 会让 99 千欧姆的 电阻器短路。 因此，放大器 电路将有 1 V/V 或 0 dB 的增益。 在低频和 高频之间， 增益将以 -20 dB/十倍频程的 速率下降。 请注意， 在频率极高时， 增益将进一步下降， 原因是放大器的 带宽限制。 请注意， 该滤波器的 截止频率是由反馈电容器 和反馈电阻器设定的。 计算出的值 是 1.005 KHz， 与 989 Hz 的 仿真值具有相关性。 值得注意的是， 滤波器将增益 从 40 dB 降至 0 dB。 衰减取决于 放大器的增益。 让我们详细 了解一下这一点。 此幻灯片比较了 反馈电容器滤波器 如何为具有高增益和 低增益的放大器工作。 在这两种情况下， 截止频率 被设定为同一个值。 正如前面 提到过的， 在高频时，反馈电容器 滤波器有效地短路了 反馈电阻器， 使增益 变为 1 V/V。 因此，反馈 电容器滤波器 会始终将增益 从直流值降至 1。 因此，滤波器的最大 衰减量等于直流增益。 在高增益 电路中， 增益从 100 V/V 衰减至 1 V/V 或 40 dB。 但是，低增益电路 只衰减了 6 dB 的 增益。 重点是，反馈 电容器滤波器 在高增益 电路中最有效。 如果您需要一个适用于 低增益电路的有效滤波器， 您也许应该研究 有源滤波器。 一般情况下，有源滤波器 比反馈电容器滤波器 更有效， 但反馈电容器 滤波器 很受欢迎，因为 它们简单且便宜。 最后，我们来探讨一下 转换速率及全功率带宽。 运算放大器的 转换速率是输出信号的 最大变化率。 如果您有兴趣 详细了解转换速率， 请观看转换速率 视频系列。 器件的转换速率 可以影响运算放大器 在不同频率下的行为， 而且此影响 可以被误解为 带宽限制。 事实上，最大输出 电压与频率的关系 取决于转换速率， 而且通常 被称为全功率带宽。 让我们来看看 全功率带宽是如何 影响两个被施加到 OPA 192 单位增益跟随器的 不同信号的。 最大输出电压 与频率的关系图 显示在给定 频率下可实现的 最大未失真峰间输出。 例如，让我们在 1 MHz 的频率下 施加一个 1 Vpk 的信号。 此信号远低于 最大输出限制， 所以不应 出现失真。 然而，在 1 MHz 频率 下的 10 Vpk 信号 是在全功率 带宽以外， 所以信号会失真。 现在，让我们 看一下时域仿真， 以了解输出在这两种 情况下会受怎样的影响。 此幻灯片显示了 频率为 1 MHz 时的 OPA 192 10 Vpk 输出 和 1 Vpk 输入。 请注意，1 Vpk 输入的输出 是 1 Vpk，符合预期。 此外，1 Vpk 输出 未显得失真。 但是，10 Vpk 输入的输出 却是 5 Vpk， 显得非常失真。 事实上，输出看起来 更像是一个三角波 而不是正弦波。 这种情况通常 发生在放大器 存在转换速率限制时。 根据上一张幻灯片中的 全功率带宽图形， 可知这些结果是有道理的。 要注意的 最后一点是， 输入信号在 OPA 192 缓冲器的带宽内。 有时候，由转换速率 限制导致的 输出信号 衰减被误解为 带宽限制。 为了避免这个 问题，请务必 确保您的输出 信号幅值不违反 数据表中给出的 最大输出电压与 频率的关系图。 总的来说，本视频 讨论了 AOL 曲线的 斜率如何影响增益带宽、 运算放大器输入电容、 计算电路的实际 增益、转换速率限制 以及一些实现 运算放大器 滤波器的简单方法。 谢谢。 请尝试完成测验以 检查您对本视频 内容的理解。